Leader-following bipartite consensus of second-order time-delay nonlinear multi-agent systems with event-triggered pinning control under signed digraph

Abstract

This paper investigates the leader-following bipartite consensus problem for second-order multi-agent systems with nonlinear dynamics, node-delay and signed digraph topology. By using pinning control strategies, an event-triggered controller is designed to achieve bipartite consensus in multi-agent systems, where a novel event-triggered function is proposed. Two cases are discussed in this paper according to whether the node-delay is differentiable or not. When the node-delay is differentiable, an LMI (Linear Matrix Inequality) condition is derived for reaching bipartite consensus in multi-agent systems by using M-matrix theory. When the node-delay is non-differentiable, some bipartite consensus conditions are developed based on Jensen inequality and the reciprocally convex approach. Moreover, it is shown that Zeno-behavior can be avoided for the designed event-triggered controller. Finally, some numerical examples are provided to illustrate the effectiveness and correctness of the theoretical analysis.